Electromagnetic Spectral Function Research Articles

Electric conductivity of QCD matter and dilepton spectra in heavy-ion collisions

The electric conductivity, σel, is a fundamental transport coefficient of QCD matter that can be related to the zero-energy limit of the electromagnetic (EM) spectral function at vanishing three-momentum in the medium. The EM spectral function is also the central quantity to describe the thermal emission rates and pertinent spectra of photon and dilepton radiation in heavy-ion collisions. Employing a model for dilepton rates that combines hadronic many-body theory with nonperturbative QGP emission constrained by lattice QCD which describes existing dilepton measurements in heavy-ion collisions, I investigate the sensitivity of low-mass dilepton spectra in Pb-Pb collisions at the CERN Large Hadron Collider (LHC) to σel. In particular, I separately evaluate the contributions from QGP and hadronic emission, and identify signatures that can help to extract σel from high-precision experimental data expected to be attainable with future detector systems at the LHC. Published by the American Physical Society 2024

Electric conductivity of hot and dense nuclear matter

Transport coefficients play an important role in characterising hot and dense nuclear matter, such as that created in ultra-relativistic heavy-ion collisions (URHIC). In the present work we calculate the electric conductivity of hot and dense hadronic matter by extracting it from the electromagnetic spectral function, through its zero energy limit at vanishing 3-momentum. We utilise the vector dominance model (VDM), in which the photon couples to hadronic currents predominantly through the ρ meson. Therefore, we use hadronic many-body theory to calculate the ρ-meson's self-energy in hot and dense hadronic matter, by dressing its pion cloud with π-ρ, π-σ, π-K, N-hole, and Δ-hole loops. We then introduce vertex corrections to maintain gauge invariance. Finally, we analyze the low-energy transport peak as a function of temperature and baryon chemical potential, and extract the conductivity along a proposed phase transition line.

Thermal dielectron measurements in Au+Au collisions at √SNN = 7.7, 14.6, and 19.6 GeV with the STAR experiment

Dielectrons emitted during the evolution of the hot and dense QCD medium created in relativistic heavy-ion collisions offer an effective way to probe the medium properties, as they do not interact via the strong force. The rate of the dielectron emission is proportional to the medium’s electromagnetic spectral function. In the dielectron invariant mass range from 400 MeV/c2 to 800 MeV/c2, the spectral function probes the in-medium ρ meson propagator which is sensitive to the medium’s properties including the total baryon density and the temperature. Meanwhile, the low energy range of the spectral function provides information about the medium’s electrical conductivity. Therefore, by measuring thermal dielectron production, we can study the microscopic interactions between the electromagnetic current and the medium. The STAR experiment has recorded large datasets of Au+Au collisions during the Beam Energy Scan Phase-II (BES-II) program, spanning center-of-mass energies between √SNN = 3.0 and 19.6 GeV with detector upgrades that benefit the dielectron measurement via extended transverse momentum and rapidity coverages as well as enhanced particle identification capability. In these proceedings, we will report on the measurements of thermal dielectrons produced in Au+Au collisions at √SNN = 7.7, 14.6, and 19.6 GeV using the STAR experiment.

Electric conductivity of hot pion matter

The determination of transport coefficients plays a central role in characterizing hot and dense nuclear matter. Currently, there are significant discrepancies between various calculations of the electric conductivity of hot hadronic matter. In the present work we calculate the electric conductivity of hot pion matter by extracting it from the electromagnetic spectral function, via its zero energy limit at vanishing 3-momentum, within the Vector Dominance Model (VDM). Since within the VDM the photon couples to the hadronic currents primarily through the ρ meson, we use hadronic many-body theory to calculate the ρ-meson's self-energy in hot pion matter, by dressing its pion cloud with thermal π-ρ and π-σ loops including vertex corrections to maintain gauge invariance. In particular, we analyze the low-energy transport peak of the spectral function, extract its behavior with temperature and compare to (the results of) existing approaches in the literature.

Electromagnetic spectral functions in hot and dense chirally imbalanced quark matter

The photon self-energy from chirally imbalanced quark matter is evaluated at finite temperature and density using the real time formulation of thermal field theory. The analytic structure is explored in detail exposing the cut structure which corresponds to a variety of physical scattering and decay processes in the medium and their thresholds. The mass of the quarks in the chiral symmetry broken phase are obtained from the gap equation of the Nambu--Jona-Lasinio model. It is found that, in presence of finite chiral chemical potential, the chiral condensate tends to get stronger at low temperatures while the opposite is observed at high temperature values. A continuous spectrum is obtained for the electromagnetic spectral function and this is purely a finite chiral chemical potential effect.

Dilepton production from chirally asymmetric matter

We evaluate the dilepton production rate (DPR) from hot and dense chirally asymmetric quark matter. The presence of a finite chiral chemical potential (CCP) in the electromagnetic spectral function results in the appearance of new cut structures signifying additional scattering processes in the medium which leads to a significant enhancement in the DPR at lower values of invariant mass. The constituent quark mass evaluated using a 3-flavour Nambu--Jona-Lasinio model is also non-trivially affected by the CCP. These are found to result in a continuous dilepton production rate as a function of the invariant mass for higher values of temperature and baryonic chemical potential.

Spectral function and dilepton rate from a strongly magnetized hot and dense medium in light of mean field models

We have calculated the electromagnetic spectral function (SF) vis-\`{a}-vis the dilepton rate (DR) by evaluating the one-loop photon polarisation tensor for a strongly magnetised hot and dense medium. The calculation is performed in the ambit of mean field models namely Nambu\textendash Jona-Lasinio (NJL) and its Polyakov loop extended version (PNJL) in the lowest Landau level approximation. These models allow for a dynamical generation of quark mass which, evidently, gets affected in the presence of a magnetised medium. We have shown that the strength of the SF gets boosted because of the presence of dynamical quarks in lieu of the current quarks. It increases as we increase the magnetic field for a given value of temperature in both NJL and PNJL models. This increment is further reflected in the DR which is enhanced as compared to the Born rate for certain values of invariant masses. We also discuss the impact of chemical potential on DR within the present scenario.

In-medium spectral functions and dilepton rates with the Functional Renormalization Group

We present recent results on in-medium spectral functions of vector and axial-vector mesons, the electromagnetic (EM) spectral function and dilepton rates using the Functional Renormalization Group (FRG) approach. Our method is based on an analytic continuation procedure that allows us to calculate real-time quantities like spectral functions at finite temperature and chemical potential. As an effective low-energy model for Quantum Chromodynamics (QCD) we use an extended linear-sigma model including quarks where (axial-)vector mesons as well as the photon are introduced as gauge bosons. In particular, it is shown how the ρ and the a1 spectral function become degenerate at high temperatures or chemical potentials due to the restoration of chiral symmetry. Preliminary results for the EM spectral function and the dilepton production rate are discussed with a focus on the possibility to identify signatures of the chiral crossover and the critical endpoint (CEP) in the QCD phase diagram.

Electromagnetic spectral function and dilepton rate in a hot magnetized QCD medium

The dilepton production rate in hot QCD medium is studied within a effective description of the medium in the presence of magnetic field. This could be done by obtaining the one-loop self energy of photon due to the effective (quasi-) quark loop at finite temperature under an arbitrary external magnetic field while employing the real time formalism of Thermal Field Theory. The effective quarks and gluons encode hot QCD medium effective in terms of their respective effective fugacities. The magnetic field enters in the form of landau level quantization, in the matter sector (quarks, antiquarks). The full Schwinger proper time propagator including all the Landau levels is considered for the quasi quarks while calculating the photon self energy. The electromagnetic Debye screening (in terms of the self-energy) has seen to be influenced both by the hot QCD medium effects and magnetic field. Analogous results are also obtained from the semi classical transport theory. The imaginary part of the photon self energy function is obtained from the discontinuities of the self energy across the Unitary cuts which are also present at zero magnetic field and the Landau cuts which are purely due to the magnetic field. The dilepton production rate is then obtained in terms of the product of electromagnetic spectral functions due to quark loop and lepton loop. The modifications of both the quarks/antiquarks as well as leptons in presence of an arbitrary external magnetic field have been considered in the formalism. Significant enhancement of the low invariant mass dileptons due the appearance of the Landau cuts in the electromagnetic spectral function at finite external magnetic field has been observed. A substantial enhancement of dilepton rate is also found when the EOS effects are considered through the effective quarks/antiquraks.

Electromagnetic spectral properties and Debye screening of a strongly magnetized hot medium

We have evaluated the electromagnetic spectral function and its spectral properties by computing the one-loop photon polarization tensor in presence of magnetic field, particularly in a strong field approximation compared to the thermal scale. When the magnetic scale is higher than the thermal scale the lowest Landau level (LLL) becomes effectively (1+1) dimensional strongly correlated system that provides a kinematical threshold based on the mass scale. Beyond this threshold the photon strikes the LLL and the spectral strength starts with a high value due to the dimensional reduction and then falls off with increase of the photon energy due to LLL dynamics in a strong field approximation. This strongly enhances the dilepton rate over the thermal perturbative leading order (Born) rate at very low invariant mass. We have also investigated the electromagnetic screening by computing the Debye screening mass and it depends distinctively on three different scales (mass of the quasiquark, temperature and the magnetic field strength) of a hot magnetized system. The mass dependence of the Debye screening supports the occurrence of a magnetic catalysis effect in the strong field approximation.

Power corrections to the electromagnetic spectral function and the dilepton rate in QCD plasma within operator product expansion in D = 4

We evaluate the electromagnetic spectral function in QCD plasma in a nonperturbative background of in-medium quark and gluon condensates by incorporating the leading order power corrections in a systematic framework within the ambit of the operator product expansion in D=4 dimension. We explicitly show that the mixing of the composite operators removes mass singularities and renders Wilson coefficients finite and well defined. As a spectral property, we then obtain the nonperturbative dilepton production rate from QCD plasma. The operator product expansion automatically restricts the dilepton rate to the intermediate mass range, which is found to be enhanced due to the power corrections. We also compare our result with those from nonperturbative calculations, e.g., lattice QCD and effective QCD models based on Polyakov loop.

Thermal electromagnetic radiation in heavy-ion collisions

We review the potential of precise measurements of electromagnetic probes in relativistic heavy-ion collisions for the theoretical understanding of strongly interacting matter. The penetrating nature of photons and dileptons implies that they can carry undistorted information about the hot and dense regions of the fireballs formed in these reactions and thus provide a unique opportunity to measure the electromagnetic spectral function of QCD matter as a function of both invariant mass and momentum. In particular we report on recent progress on how the medium modifications of the (dominant) isovector part of the vector current correlator ($\rho$ channel) can shed light on the mechanism of chiral symmetry restoration in the hot and/or dense environment. In addition, thermal dilepton radiation enables novel access to (a) the fireball lifetime through the dilepton yield in the low invariant-mass window $0.3 \; \mathrm{GeV} \leq M \leq 0.7 \; \mathrm{GeV}$, and (b) the early temperatures of the fireball through the slope of the invariant-mass spectrum in the intermediate-mass region ($1.5 \; \mathrm{GeV} <M< 2.5 \; \mathrm{GeV}$). The investigation of the pertinent excitation function suggests that the beam energies provided by the NICA and FAIR projects are in a promising range for a potential discovery of the onset of a first order phase transition, as signaled by a non-monotonous behavior of both low-mass yields and temperature slopes.

Update on Chiral Symmetry Restoration in the Context of Dilepton Data

We evaluate currently available information on low-mass dilepton and direct-photon emission spectra measured in ultrarelativistic heavy-ion collisions. In the first part an attempt is made to develop a consistent picture of the in-medium effects on the electromagnetic spectral function and pinpoint its emission history by utilizing its radial and elliptic flow signatures. In the second part we elaborate on the implications of the empirical information on the nature of chiral symmetry restoration. We indicate how the melting of the ρ resonance in hot and dense matter is related to, and compatible with, the reduction of chiral order parameters as "measured" in thermal lattice QCD.

Theory of Soft Electromagnetic Emission in Heavy-Ion Collisions

A status report of utilizing soft electromagnetic radiation (aka thermal photons and dileptons) in the diagnosis of strongly interacting matter in ultrarelativistic heavy-ion collisions is given. After briefly elaborating on relations of the electromagnetic spectral function to chiral symmetry restoration and the transition from hadron to quark degrees of freedom, various calculations of electromagnetic emission rates in the hadronic and quark-gluon plasma phases of QCD matter are discussed. This, in particular, includes insights from recent thermal lattice QCD computations. Applications to dilepton and photon spectra in heavy-ion collisions highlight their role as a spectro-, thermo-, baro- and chrono-meter of extraordinary precision.

A spectral function for an interacting electron-lattice system

The lattice quasiparticle conserving Hamiltonian for an interacting electron-lattice system is employed in calculating the electromagnetic spectral response function in absorption for an electron located in a deep trap such that the electronic transition energies are much higher than the cutoff of the lattice vibrational spectrum. The zero-order Hamiltonian for the system is then diagonal in electronic quantum numbers and linear in the lattice vibrational mode coordinates. The spectral response is calculated for a dipole mediated transition by employing the temperature-dependent double-time Green's function technique. It is shown that because of the properties of the lattice field operators, the hierarchy of Green's function equations decouples and no higher-order Green's functions are required for obtaining an explicit solution to a given order. An exact solution for the absorption of spectrum in the lowest order in electromagnetic field is given in terms of delta-function lines. Broadening effects, numerical calculation restrictions and applications to molecular vibronic spectra are briefly discussed.

Spectral function sum rules in quantum chromodynamics (II). Flavour components of the electromagnetic current

Sum rules of the algebra of currents of the type of the Das, Mathur, Okubo sum rule are reconsidered in the light of quantum chromodynamics (QCD). These sum rules are replaced by new finite-energy sum rules which equate differences of definite integrals of the various flavour components of the electromagnetic spectral function to functions explicitly calculated in perturbative QCD. Phenomenological applications of these sum rules are discussed.